Question: 1. How many ways are there of choosing, with order, the even integers out of the integers 1 through 12?
2. We have seen that n! increases at a fast pace as n is chosen larger. Because factorials arise in many contexts, there are formulas that can be used to approximate n! when n is large, but which can be computed in fewer steps than it takes to compute n! as the product of the integers from 1 through n. Stirling's formula states that
n! ≈ (n/e)n √(2Πn),
with accuracy improving as n is chosen larger. To test this supposition, make a three column table, having values of n for n = 1, 2... 20 in the first column. In the second column, compute n!, and in the third column, the Stirling approximation. Compute the percentage error in the approximation in each case.